Yes, corkcambium only produces cork which it does on its outer side (the outer layer of a tree's bark) which is only several cell layers deep. Whereas the vascular cambium produces both secondary xylem(sapwood/heartwood) and secondary phloem(inner bark).

For my first post I want to throw my two cents in. In this case just some synonyms, corkcambium is also known as phellogen, cork is also known as phellum and as MrMistery mentioned phelloderm is phelloderm.

Oh, and for interests sake all of the above combined with the secondary phloem is commonly known as 'bark'.